new_x_concatenated_sequence
- qctrlopencontrols.new_x_concatenated_sequence(duration, concatenation_order, pre_post_rotation=False, name=None)[source]
Creates the \(X\)-concatenated sequence.
- Parameters:
duration (float) – The total duration of the sequence \(\tau\) (in seconds).
concatenation_order (int) – The number of concatenation of base sequence.
pre_post_rotation (bool, optional) – If
True, a \(X_{\pi/2}\) rotation is added at the start and end of the sequence. Defaults toFalse.name (string, optional) – Name of the sequence. Defaults to
None.
- Returns:
The \(X\)-concatenated sequence.
- Return type:
See also
Notes
The \(X\)-concatenated sequence [1] is constructed by recursively concatenating control sequence structures. It’s parameterized by the concatenation order \(l\) and the duration of the total sequence \(\tau\). Let the \(l\)-th order of concatenation be denoted as \(C_l(\tau)\). In this scheme, zeroth order concatenation of duration \(\tau\) is defined as free evolution over a period of \(\tau\). Using the notation \({\mathcal 1}(\tau)\) to represent free evolution over duration \(\tau\), the the base sequence is:
\[C_0(\tau) = {\mathcal 1}(\tau) \;.\]The \(l\)-th order \(X\)-concatenated sequence can be recursively defined as
\[C_l(\tau) = C_{l - 1}(\tau / 2) X_{\pi} C_{l - 1}(\tau / 2) X_{\pi} \;.\]References